# Design of Capacitive Bridge Fault Current Limiter for Low-Voltage Ride-Through Capacity Enrichment of Doubly Fed Induction Generator-Based Wind Farm

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## Abstract

**:**

## 1. Introduction

## 2. DFIG Farm Model

#### 2.1. Turbine Model

_{m}) by WT and given by Equation (1):

_{w}is the speed of wind, A is the rotor swept area, and C

_{P}is the power coefficient. Here, wind speed is assumed to be constant, i.e., reference is taken as constant accelerating turbine. The power coefficient is given a best suitable value so that functioning of wind speed gives a maximum extractable power.

#### 2.2. DFIG Model

_{s}and V

_{r}), and fluxes (λ

_{s}and λ

_{s}) in the synchronous reference frame are represented [49] by Equations (2)–(5):

_{s}and L

_{s}are stator resistance and leakage inductance. Similarly, rotor resistance and leakage inductances are R

_{r}and L

_{r}. L

_{m}is the magnetizing inductance, whereas stator and rotor angular frequencies are denoted by ω

_{s}and ω

_{r}. By ignoring stator and rotor resistances, combining Equations (2) and (3) gives Equation (6):

#### 2.3. DFIG Control

#### 2.4. Control of Pitch Angle

## 3. CBFCL Operation and Design

_{1}-D

_{4}) and switching IGBT(T), and is in sequence with the DC reactor. The capacitor (C

_{sh}) is in sequence with resistor (R

_{sh}), and is linked across the bridge circuit. The following modes discuss the operation of CBFCL.

#### 3.1. Normal Operating Mode

_{1}-L

_{d}-r

_{d}-T-D

_{4}and D

_{2}-L

_{d}-r

_{d}-T-D

_{3}during positive and negative half cycles, respectively. The DC reactor current (i

_{d}) is provided by the bridge circuit and charged to line current (i

_{0}). Due to the large impedance shunt path, bridge circuits have a maximum line current and negligible line current in the shunt path. There are some losses due to the presence of reactor resistance and switching, but these are irrelevant compared to line drop and losses.

#### 3.2. Fault Operating Mode

_{dc}restricts its expanding rate and insures the semiconductor switch against extreme di/dt toward the start of the fault event. When the current goes to the greatest admissible fault current, I

_{m}, which is determined by the administrator, the control arrangement of the semiconductor switch turns it off. Along these lines, the bridge withdraws from the feeder, and shunt impedance enters into the faulted line and limits fault current. The characteristic of DC reactor impeded this sudden change, and meanwhile instantaneous voltage sag is suppressed by CBFCL. An increase in DC reactor current given as:

_{d}is average value of source voltage and t

_{0}is time when fault is detected. Whenever i

_{d}reaches the threshold value (i

_{T}), the CBFCL control system shown in Figure 2b produces a gate signal to turn off IGBT. At this the time bridge circuit is opened and the limiting impedance is introduced in sequence with a line to limit the short circuit current.

#### 3.3. Recovery Mode

_{T}), IGBT receives a huge voltage signal pulse, making it activate and system restore to the usual operating mode. The advantage of a capacitive bridge is that it helps to gain a fast recovery voltage with huge improvements in the stability of the power system.

#### 3.4. L_{d}, R_{sh}, C_{sh} Design

_{d}is the change between pre-fault value and threshold value and T

_{d}is the fault detection time delay. Figure 2c represents the equivalent model to the test system under study during fault conditions. In this condition, the shortcoming line transports the power. To consume the active power, R

_{sh}will be sufficient to cause the least disturbance, and C

_{sh}will also provide necessary reactive power:

## 4. Simulation Results

- Circumstance A: without FCL.
- Circumstance B: with IBFCL.
- Circumstance C: with CBFCL.
- Circumstance D: with CBFCL using Fuzzy controller in drive train.

#### 4.1. Variation of PCC Voltage, DC Link Voltage, Rotor Speed with Time

#### 4.2. Variation of Rotor Current with Time for Different Circumstances

#### 4.3. Variation of Reactive Power, Reactive Power Flow in Line, Active Power with Time

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

FCL | fault current limiter |

IBFCL | inductive bridge fault current limiter |

CBFCL | capacitive bridge fault current limiter |

DFIG | doubly fed induction generator |

FRT | fault ride through |

RSC | rotor side converter |

GSC | grid side converter |

LVRT | low voltage ride through |

STATCOM | static synchronous compensator |

WF | wind farm |

SDBR | series dynamic breaking resistor |

PCC | point of common coupling |

DVR | dynamic voltage restorer |

UPIC | unified power inline controller |

IGBT | insulated gate bipolar thyristor |

## Appendix A

Specifications of DFIG | Specifications of CBFCL and Grid | ||||||
---|---|---|---|---|---|---|---|

Nominal power | 2 MVA | Nominal voltage | 66 KV | ||||

Nominal voltage | 690 V | Nominal frequency | 50 hz | ||||

X_{ls} | 0.1022 pu | Transformer ratio | 690/66 KV | ||||

X_{lr} | 0.1123 pu | Resistance(R) | 1.5 ohm | ||||

R_{s} | 0.0074 pu | Reactance (X) | 3.4 ohm | ||||

R_{r} | 0.0061 pu | R_{sh} | 10 ohm | ||||

H | 3 s | C_{sh} | 50 microF | ||||

X_{m} | 4.6321 pu | L_{D} | 0.01 H | ||||

RSC of DFIG | GSC of DFIG | ||||||

Kp1 | 0.25 | Ki1 | 25 | Kp1 | 0.25 | Ki1 | 50 |

Kp2 | 1.3 | Ki2 | 100 | Kp2 | 0.25 | Ki2 | 120 |

Kp3 | 0.5 | Ki3 | 10 | Kp3 | 0.75 | Ki3 | 100 |

Kp4 | 0.12 | Ki4 | 125 | Kp4 | 0.5 | Ki4 | 150 |

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**Figure 1.**(

**a**) Simplified circuit diagram of DFIG, (

**b**,

**c**) RSC controller, (

**d**,

**e**) GSC control systems, and (

**f**) pitch angle control with fuzzy.

**Figure 2.**(

**a**) Normal operating mode. (

**b**) Event at fault mode. (

**c**) Test system equivalent circuit at the time of fault. (

**d**) Simulated power system.

**Figure 4.**Rotor currents vs time in (

**a**) circumstance A, (

**b**) circumstance B, (

**c**) circumstance C, and (

**d**) circumstance D.

**Figure 5.**(

**a**) Active power vs time. (

**b**) Reactive power vs time. (

**c**) Reactive power flow in line1 vs time.

NL | NS | ZR | PS | PL | |
---|---|---|---|---|---|

NL | PS | ZR | ZR | NS | NS |

NS | PL | PS | ZR | ZR | PS |

ZR | ZR | ZR | NS | ZR | ZR |

PS | PS | NS | ZR | PS | PS |

PL | NS | ZR | PS | ZR | NL |

**Table 2.**Variation in PCC voltage, DC link voltage, and rotor speed with time in different circumstances.

Time (Sec) | PCC Voltage (Vs) Time | Dc Link Voltage (Vs) Time | Rotor Speed (Vs) Time | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

A | B | C | D | A | B | C | D | A | B | C | D | |

10 | 1 | 1 | 1 | 1 | 1 | 0.95 | 1 | 1.07 | 1.075 | 1.075 | 1.075 | 1.075 |

10.1 | 0.1 | 0.8 | 0.98 | 0.99 | 1.4 | 1.2 | 1.1 | 1.075 | 1.15 | 1.08 | 1.072 | 1.072 |

10.2 | 0.8 | 0.9 | 0.98 | 0.99 | 1.6 | 1.2 | 1.18 | 1.08 | 1.22 | 1.09 | 1.072 | 1.072 |

10.3 | 0.8 | 0.95 | 0.99 | 1 | 1.2 | 0.91 | 1.1 | 1.06 | 1.17 | 1.072 | 1.073 | 1.073 |

10.4 | 0.9 | 0.95 | 0.99 | 1 | 0.9 | 0.9 | 1 | 1.052 | 1.08 | 1.075 | 1.075 | 1.075 |

10.5 | 0.98 | 0.98 | 0.99 | 1 | 0.9 | 0.9 | 1 | 1.03 | 1.075 | 1.075 | 1.075 | 1.075 |

Time (Sec) | Rotor Current | |||
---|---|---|---|---|

A | B | C | D | |

10 | 3 | 1.4 | 1.02 | 1.01 |

10.1 | 2 | 1.3 | 1.02 | 1.01 |

10.2 | 1.5 | 1.2 | 1.01 | 1.01 |

10.3 | 1.3 | 1.05 | 1.01 | 1.01 |

10.4 | 1.2 | 1 | 1 | 1 |

10.5 | 1 | 1 | 1 | 1 |

**Table 4.**Variation in reactive power, reactive power flow in line, and active power with time in different circumstances.

Time (Sec) | Wind Farm Reactive Power (Vs) Time | Reactive Power Flow in Line (Vs) Time | Wind Farm Active Power (Vs) Time | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

A | B | C | D | A | B | C | D | A | B | C | D | |

10 | 0 | 0 | 0.145 | 0.132 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |

10.1 | 0 | 0 | 0.145 | 0.132 | 0 | −0.5 | 0.5 | 0.35 | 0 | 0.4 | 0.2 | 0.15 |

10.2 | −2 | −0.8 | 0 | 0 | −2 | −0.3 | 0.3 | 0.23 | 2 | 1.5 | 1.2 | 1.05 |

10.3 | −2.5 | −0.2 | 0 | 0 | −1.7 | −0.1 | 0.2 | 0.15 | 1.6 | 0.8 | 0.6 | 0.5 |

10.4 | −2.2 | −0.1 | 0 | 0 | −1.5 | −0.1 | 0 | 0 | 2 | 1.2 | 1.1 | 1.05 |

10.5 | −1.5 | −0.1 | 0 | 0 | −1.2 | −0.1 | 0 | 0 | 1.8 | 1.2 | 0.95 | 0.98 |

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**MDPI and ACS Style**

Padmaja, A.; Shanmukh, A.; Mendu, S.S.; Devarapalli, R.; Serrano González, J.; García Márquez, F.P.
Design of Capacitive Bridge Fault Current Limiter for Low-Voltage Ride-Through Capacity Enrichment of Doubly Fed Induction Generator-Based Wind Farm. *Sustainability* **2021**, *13*, 6656.
https://doi.org/10.3390/su13126656

**AMA Style**

Padmaja A, Shanmukh A, Mendu SS, Devarapalli R, Serrano González J, García Márquez FP.
Design of Capacitive Bridge Fault Current Limiter for Low-Voltage Ride-Through Capacity Enrichment of Doubly Fed Induction Generator-Based Wind Farm. *Sustainability*. 2021; 13(12):6656.
https://doi.org/10.3390/su13126656

**Chicago/Turabian Style**

Padmaja, A., Allusivala Shanmukh, Siva Subrahmanyam Mendu, Ramesh Devarapalli, Javier Serrano González, and Fausto Pedro García Márquez.
2021. "Design of Capacitive Bridge Fault Current Limiter for Low-Voltage Ride-Through Capacity Enrichment of Doubly Fed Induction Generator-Based Wind Farm" *Sustainability* 13, no. 12: 6656.
https://doi.org/10.3390/su13126656